Pion Structure in Minkowski space

Name: Pion Structure in Minkowski space
Start: 2022-01-19T13:30:00+00:00
End: 2022-01-19T15:30:00+00:00
Location: No location set

by Wayne de Paula (Instituto Tecnologico de Aeronautica, Brazil)

Wednesday Jan 19, 2022, 1:30 PM → 3:30 PM GMT

Description

A dynamical approach applied to describe the pion based on the solution of the Bethe-Salpeter equation (BSE) in Minkowski space is reviewed. The main ingredient is the so-called Nakanishi integral representation of the Bethe-Salpeter amplitude, which allows to establish the formal bridge between the BSE and its projection on the null plane, and to ultimately set up the numerical evaluation.

In the way to elaborate the integral equations for the Nakanishi weight functions, end-point singularities have to be addressed carefully [1], so that the obtained equations become amenable to numerical treatments.

We adopted an interaction kernel built with constituent quarks and one gluon exchange. In addition, the chosen quark-gluon vertex is the leading longitudinal component, as suggested by a combined analysis of lattice QCD simulations and Dyson-Schwinger equations for the quark propagator [2].

The solution of the pion BSE in Minkowski allowed us to directly access several observables. Among them, the weak decay constant, the valence probability, the LF-momentum distributions, the distribution amplitudes, the probability densities both in the LF-momentum space and in the 3D space (given by the Cartesian product of the covariant Ioffe-time and transverse coordinates) [3] and the electromagnetic form factor, which is found to be in good agreement with available experimental data [4].

The next step in our program involves the consideration of the quark dressing in Minkowski space. We present some preliminary results of the quark self-energy from the solution of the Schwinger-Dyson Equation in Minkowski space which is tuned to reproduce the Lattice running quark mass for space-like momentum. Such propagators will be included in our future studies of the pion, which will be briefly sketched.

References:

1. W. de Paula, T. Frederico, G. Salme and M. Viviani, Phys. Rev. D 94 (2016) ,071901(R)

2. O. Oliveira, T. Frederico and W. de Paula, Eur. Phys. J. C 80 (2020) 484

3. W. de Paula, E. Ydrefors, J. H. Alvarenga Nogueira, T. Frederico and G. Salme, Phys. Rev. D 103 (2021) 014002

4. E. Ydrefors, W. de Paula, J. H. A. Nogueira, T. Frederico and G. Salme, Phys. Lett. B 820 (2021) 136494

Webinar at https://us02web.zoom.us/j/81572103194?pwd=eE1QVWZFc1hWbWszZ2N0RW1iWHFBZz09